syms x;
You created x as a scalar symbolic variable.
soln = ode45(@Problem03ODEFunction,[0 10],[0;0;0]);
You calculate the solution to an ode problem, assigning the solution to soln
y = x(:, 1); % y(t)
You index the scalar symbolic variable x, which you have not changed anywhere in your code. In particular, x is not the output from the ode45 call.
When you use a single output for ode45() it outputs a solution object, which you would manipulate with tools such as deval
if t>=1 && t<10
ft=1;
else
ft=0;
end
The mathematics of ode45 and all Runge Kutta methods, requires that the first two derivatives of the provided expressions must be continuous. If you are lucky then ode45() will notice and give you an error message. If you are not lucky, such as in your code, then ode45() will simply give you the wrong results without warning you that your output is nonsense.
You need to stop the first ode45() call at t = 10 seconds, and take the output you get and input it to a second ode45() call that uses the 0 for ft for the rest of the time. That is relatively easy for this case as the boundaries are strictly time-based: just be careful with what tspan you pass in. In the more general case where you need to determine dynamically whether you have encountered a boundary (such is the case for a bouncing ball) then you would need to use event functions.
